Theorems · Definition · group theory
AddSubgroup.fintypeQuotientOfFiniteIndex
{G : Type u_1} → [inst : AddGroup G] → {H : AddSubgroup G} → [H.FiniteIndex] → Fintype (G ⧸ H)A finite index subgroup has finite quotient
- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement · cited by 7,736
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- AddSubgroup.FiniteIndexstatement and proof · cited by 66
- AddSubgroup.FiniteIndex.index_ne_zeroproof · cited by 10
- AddSubgroup.fintypeOfIndexNeZeroproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.leftTransversals.diffproof · cited by 5
- AddSubgroup.leftTransversals.vadd_diff_vaddproof · cited by 1
- ProperlyDiscontinuousVAdd.ofFiniteRelIndexproof · cited by 1
- AddSubgroup.exists_finset_card_le_addproof · cited by 0